Derringer and Suich ( “ Simultaneous Optimization of Several Response Variables, ” Journal of Quality Technology , 1980) studied the relationship of an abrasion index for a tire tread compound in terms of three factors: x1 , hydrated silica level; x2 , silane coupling agent level; and x3 , sulfur level. The following table gives the actual results.

a. Perform a thorough analysis of the results including residual plots.

b. Perform the appropriate test for lack of fi t.

x X2 X3 y -1 -1 1 102 1 -1 120 -1 1 117 1 198 103 132 -1 1 132 1 -1 139 0 0 0 133 0 0 133 0 0 140 0 0 0 000 0 142 0 145 0 142